I don't have a comparative advantage in doing this, so why not see if I can find someone who does?
If you are interested in Canadian monetary policy, and have basic econometric skills, you should be able to do this. And the answer you come up with might be interesting.
1. Read my old post (or posts, by just typing "core" in the search box on the right) on how we could properly test whether it is core or total inflation (or both) that central banks should be looking at when they decide on monetary policy. Remember that there's a distinction between what variable the central bank should be targeting (should it try to hold total inflation or core inflation constant at 2%?), and what indicator variable(s) the central bank should be looking at when it adjusts monetary policy to try to hit that target (if total inflation rises, and core inflation falls, should the bank tighten or loosen to hit its target?). The Bank of Canada has already answered the first question, by deciding to target total inflation. You are trying to help answer the second question: what should it look at and respond to if it wants to target total inflation? Before doing any econometrics you must first get a rough idea of why you are doing it and what the results might mean.
2. Get monthly data for the last (say) 20 years on: CPI inflation; core CPI inflation; the Bank of Canada overnight rate; and maybe a couple of other variables that you think the Bank of Canada might look at when setting the overnight rate (like unemployment rate and exchange rate?).
3. Estimate the Bank of Canada's reaction function. You are trying to find out whether the Bank of Canada has in fact responded to total and/or core inflation in the past, and how strongly it has responded to each. Remember that Statistics Canada publishes data with a lag, and there's a lag between the data being published and the Bank's next Fixed Announcement Date, and a lag between FADs. So there is no way the June overnight rate can respond to the June inflation rate. There will be a lag in the response. My guess is a couple of months. You might want to add other variables to the right hand side of the equation that you think the Bank might also respond to. Maybe unemployment rate and exchange rate? You might find the equation works better with the lagged overnight rate on the right hand side as well. Your call.
4. Estimate an "inflation forecasting equation". Remember that the Bank of Canada is supposed to be targeting 2% CPI inflation at a (roughly) two-year horizon. If the Bank of Canada is responding perfectly to the information it has available, deviations of CPI inflation from the 2% target should be unforecastable from anything the Bank had information on when it set the overnight rate two years back. That's testable. See what happens when you run a regression of inflation minus 2% on two year ago information, like total and core inflation. For example, if you find that core inflation is a good forecaster of two year ahead total inflation (with a positive sign) that means the Bank should have been responding more strongly to core than it actually did.
5. Report back your results. Don't be surprised if your results come out weird or meaningless; that's an occupational hazard. Don't be surprised if everybody else says you did it wrong, and suggests all sorts of possible changes to your regression equations; that too is an occupational hazard. (Actually, more of a certainty than a hazard, because they always do this.) Don't blame me if the whole thing turns out to be a waste of time; that too is an occupational hazard. Empirical work is risky.